At 40 metres thick, the Ward Hunt Ice Shelf is estimated to be 3,000 to 5,000 years old, jutting off the island like an extension of the land.

The key detail was the age of the ice shelf. Being 3000 to 5000 years old correlates very well with the existence of the Holocene climatic optimum. This data is confirmed from several sources, including references several decades old:

Radiocarbon dates and glaciological features of the Ward Hunt area along northernmost Ellesmere Island suggest the following chronology, which is consistent with world-wide climatic oscillations: 1) 10,000-4100 B.P.: deglaciation, and development of several marine levels, particularly one now 40 m. above sea level, at 7500+-300 B.P.; 2) 4100-2400 years B.P.: climatic deterioration, glacial readvance and formation of ice shelves; 3) 2400-1400 years B.P.: general climatic amelioration; development of dust ablation horizon on Ward Hunt Ice Shelf, glacial retreat; 4) 1400 B.P. - present : climatic deterioration, with renewed thickening of Ward Hunt Ice Shelf, and beginnings of growth of ice rises; the last-mentioned experienced maximum growth in the interval between 350-170 years ago; slight glacial readvance.

The specimen represents an early Holocene range extension of 400–700 km over the present. Because the narwhal requires abundant open water to survive, the Holocene tusk is an important independent item of proxy data on palaeoclimatic change. Contemporary migration routes are directly related to seasonal sea ice in the inter-island channels of the central Canadian Arctic archipelago. The presence of a narwhal on the northwest Ellesmere Island coast at 6,830 ± 50 B. P. suggests that sea ice and ice-shelf conditions were more favourable at that time. A comprehensive chronological framework for late Quaternary and Holocene geomorphic/climatic events from northern Ellesmere Island records a warm early Holocene characterized by abundant driftwood entry into the high Arctic.

The same issues can naturally be also found for the Nares Strait, where the Petermann glacier drains. A paper by John England, referenced in the CBC article above, doesn't leave any doubts about what was going on several millenia ago:

Re-entry of the sea throughout Nares Strait is shown by a series of paleogeographic maps based on geomorphic evidence and radiocarbon dates on shells associated with marine limit. Deglaciation at the north end of the strait occurred by 10.1 ka BP and, at thesouth end, by 9.0 ka BP. Nares Strait may still have been blocked by ice north of Kane Basin at 8 ka BP, however by 7.5 ka BP it provided an unobstructed seaway from the Arctic Ocean to Baffin Bay.

Palaeoceanographic reconstructions from dinocyst assemblages show that from ~6.5 to 3.3 ka BP, there were large oscillations in summer sea surface temperature (SST) from 3 °C cooler than now to 6 °C warmer, and that variations in SIC ranged from two months more to four months less of heavy ice compared to now.

While it is sad that ice sheets are melting, it's nothing new for Nature. In historical terms, ice sheets have gone, and gotten back. One might just wonder what was causing climate change then? Or understand that this melting may even be good for science, as collecting samples from where ice is gown, will certainly reveal our past history in more detail...